Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

a (35 - a) = 300 - a^{2} + 35 a - 300 = 0 a^{2} - 35 a + 300 = 0 p = 1; q = - 35; r = 300 D = q^{2} - 4 p r = 3 5^{2} - 4 \cdot 1 \cdot 300 = 25 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{3 5 \pm 2 5}{2} a_{1, 2} = \frac{3 5 \pm 5}{2} a_{1, 2} = 17.5 \pm 2.5 a_{1} = 20 a_{2} = 15 Factored form of the equation: (a - 20) (a - 15) = 0

Solution in text:

-a²+35a-300=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 25
D > 0 ... The equation has two distinct real roots

a₁ = 20
a₂ = 15

P = {20; 15}